A4For any two finite sets A and B, define f(A,B) to be the number of elements that are contained either in A or in B, but not in both A and B. Three given sets X, Y and Z satisfy f(X, Y ) = f(Y,Z) = f(Z,X). (a) Prove that f(X, Y ) is even. (b) Find a set W such that f(W,X) = f(W, Y ) = f(W, Z) = 0.5 f(X, Y ).

A4For any two finite sets A and B, define f(A,B) to be the number of elements that are contained either in A or in B, but not in both A and B. Three given sets X, Y and Z satisfy f(X, Y ) = f(Y,Z) = f(Z,X). (a) Prove that f(X, Y ) is even. (b) Find a set W such that f(W,X) = f(W, Y ) = f(W, Z) = 0.5 f(X, Y ).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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